WittSem 100L
Patterns in Nature: From Snowflakes to Galaxies- Fall
2007
Instructor: Dr. Elizabeth George, Science 308B, 327-7854, egeorge@wittenberg.edu
Web
page: http://userpages.wittenberg.edu/egeorge/WTSM100.html
Office hours: I’m usually in or around my office when I’m not
in class or have other obligations such as meetings. I’ll make my schedule
available soon. Also, feel free to make an appointment with me.
Course time and location: Tuesday/Thursday, 9:40-11:10, Science 261
What’s this course about?
From childhood, human beings are fascinated by patterns in the world around us: striped and spotted animals, one-of-a-kind snowflakes, swirling wisps of clouds, the songs of birds. In this course, we'll explore how such patterns develop in nature, and how we can describe and understand them. We'll learn how surprisingly complex patterns can be produced from simple rules. We'll also discuss why we find some patterns to be more pleasing than others, and ways in which our senses and brain affect how we perceive the world (even causing optical and auditory illusions). We'll make connections between nature, art, and mathematics through classroom activities, discussions, readings, and field trips. A term project will give you an opportunity to apply the ideas learned in this course to a subject that you're interested in. (Projects are possible in a wide range of areas, including science, art, music, mathematics, economics, computer science, etc.) No specific background is needed for this course: the only prerequisites are curiosity and a willingness to explore.
Course goals:
Appreciate the
interconnectedness of ideas and knowledge
See a variety of approaches
to the same phenomena, and master some of these approaches
Develop reasoning, reading,
and communication skills
Nurture curiosity,
creativity, and openness to new ideas
Required course
materials:
Readings from various sources
will be made available as needed.
Access to a calculator will
be helpful.
Grading policy: Grades will be based on the following:
|
Assignments (in and out of
class) |
25% |
|
Class
attendance/participation |
10% |
|
3 exams (equally weighted) |
45% |
|
Project |
20% |
|
TOTAL |
100% |
Letter grades will be
assigned according to the following scale: 100% ≥ A ≥ 90%, 90% >
B ≥ 80%, 80% > C ≥ 70%, 70% > D ≥ 60%, 60% > F. A score within 3 percentage points of a
boundary will receive a + or grade (for
example, the A- range will extend from 90 to 93%).
Project: One of the exciting things about this subject is that with even a little knowledge you can quickly get into interesting research problems and applications to other fields. You’ll do a project that will let you apply these ideas to a specific topic that you’re interested in--choosing the topic in consultation with me. You’ll present your results to the rest of the class in a special poster session at the end of the semester. I’ll give you more details and a timetable during the first few weeks of class.
Math-Reasoning-Intensive Course: This is a math-reasoning-intensive course, which means that we will use the language of mathematics as a means of investigation and communication throughout. In order to receive M-credit for this course, your math placement score must be 22 or higher before the second exam. If you are not at this level yet, you抣l need to go to the Math Workshop (218 Hollenbeck, 327-6155) to work on raising your score. (http://www4.wittenberg.edu/administration/math_workshop/)
Disabilities: If you have a documented disability and need to arrange reasonable accommodations, please contact all of your instructors as soon as possible. Retroactive accommodations will not be given. Please contact Lisa Rhine, Assistant Provost for Academic Services at (937) 327-7924 in room 208 Recitation Hall to coordinate accommodations and receive self-identification letters for each professor.
Academic expectations:
Time management: In college, you don’t spend as much time in class as in high school, but we expect you to accomplish a lot--which means you’re responsible for doing more of your work outside of class. The standard college-level expectation is to spend an average of 2-3 hours outside of class (reading, solving problems, working on class presentations, preparing for exams, etc.) for every hour in class (except for labs and studio courses).
Taking care of yourself: Getting enough sleep and otherwise taking care of yourself so that you can function well is part of your job as a student.
Class attendance: Lots of research shows that class attendance and grade are related, even for courses where attendance is not required. I expect that you’ll be in class unless you have a situation that justifies an excused absence (illness, University-sponsored event, death in the family, observance of a religious holiday). In particular, if you are going to miss an exam for such a reason, you must tell me (or leave a message by email or phone) before the exam in order to be eligible for a makeup exam.
Use the resources available to you: Learning is ultimately your responsibility, but you have many resources available to help you. In particular, your professors are here at Wittenberg because they enjoy teaching and working with students, so don’t hesitate to take advantage of their interest and their expertise!
Academic Integrity: Responsible learners and researchers uphold high standards of integrity. Therefore, all exams and certain assignments will carry the Wittenberg Honor Statement:
I affirm that my work upholds the highest standards of honesty and academic integrity at Wittenberg, and that I have neither given nor received any unauthorized assistance.
I expect that you will be able to affirm this statement for each of these exams and assignments. We’ll talk about standards for academic integrity as we go along. For general information, see http://www4.wittenberg.edu/academics/academicintegrity/. Most important, please ask if anything isn’t clear.
http://www.its.caltech.edu/~atomic/snowcrystals/
Tentative Schedule
|
Week |
Topic |
|
0 |
Introduction to the course: themes & concepts |
|
|
Part I: Space, size, and patterns |
|
1 |
Space and scale (Stevens, Ch. 1) |
|
2 |
Basic patterns: spirals, meanders, explosions,
branches (Stevens, Ch. 2 & 4) |
|
3 |
|
|
4 |
|
|
5 |
Tilings: from beehives to Escher
(Peterson, Ch 1; Livio, Ch. 8)
Exam 1 |
|
|
Part II: Patterns and perception |
|
6 |
The Golden Ratio in nature and
art (Livio, Ch. 1 & 2)
|
|
7 |
Rabbits, sunflowers, and galaxies (Livio, Ch.
5; Burger, Ch. 6) |
|
8 |
Aesthetics: connections between nature, mathematics,
and the arts (Livio, Ch. 7; Burger, Ch. 7) |
|
9 |
Fall
Break Perception and illusions (supplemental articles) |
|
10 |
Perception
and illusions
Exam 2
|
|
|
Part III: Complexity from simplicity
|
|
11 |
Clouds are not spheres: the
fractal geometry of nature (Peterson, Ch. 5; supplemental articles)
|
|
12 |
How to make a snowflake: the collage theorem,
fractal geometry, and computer graphics (supplemental articles) |
|
13 |
Cellular automata: Artificial life and how the
leopard got his spots (Peterson, Ch. 7; Gribbin) |
|
14 |
The universe in a grain of sand:
the Mandelbrot set (Peterson, Ch. 6)
Thanksgiving break |
|
15 |
Exploring
the Mandelbrot set
Exam 3
|
|
16 |
Project meetings
|
Project presentations will
be given during the final exam period: 3:30-6:30 p.m., Thursday, December 13.
I am satisfied with the mystery of life's eternity and with a knowledge, a sense, of the marvelous structure of existence as well as the humble attempt to understand even a tiny portion of the reason that manifests itself in nature.
Albert Einstein, in The World As I See It